Phase Transitions and the Search Problem

@article{Hogg1996PhaseTA,
  title={Phase Transitions and the Search Problem},
  author={Tad Hogg and Bernardo A. Huberman and Colin P. Williams},
  journal={Artif. Intell.},
  year={1996},
  volume={81},
  pages={1-15}
}

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References

SHOWING 1-10 OF 68 REFERENCES
THE TYPICALITY OF PHASE TRANSITIONS IN SEARCH
TLDR
A criterion for determining when average case results reflect typical behavior is introduced which allows the method developed here to be used for investigating other large‐scale behaviors of complex AI systems.
Applications of Statistical Mechanics to Combinatorial Search Problems
The statistical mechanics of combinatorial search problems is described using the example of the well-known NP-complete graph coloring problem. We focus on a recently identified phase transition from
Optimization by Simulated Annealing
TLDR
A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems.
Quantum Computing and Phase Transitions in Combinatorial Search
  • T. Hogg
  • Computer Science
    J. Artif. Intell. Res.
  • 1996
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done
The phase transition in constraint satisfaction problems: A closer look at the mushy region
This paper examines the phase transition, in which the probability that there is a solution decreases from 1 to 0 as the constraints become increasingly tight, for a class of binary constraint
Observation of Phase Transitions in Spreading Activation Networks
TLDR
This work has confirmed a predicted abrupt behavioral change as either the topology of the network or the activation parameters are varied across phase boundaries in spreading activation networks.
...
1
2
3
4
5
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